Bring approximately 2 quarts salted water to boil.
Trim ends of unpeeled eggplants.
Cut each eggplant in half lengthwise, then cut halves into 3 lengthwise slices.
Boil, uncovered, 3 to 5 minutes; then refresh under cold running water and pat dry.
Brush slices on all sides with olive oil.
Sprinkle with salt, pepper, oregano, and marjoram.
Set oven to Broil.
Place on baking sheet and broil 2 to 3 minutes.
Turn and broil 2 to 3 more minutes.
Sprinkle with Parmesan cheese and serve.